Anal. Chem. 1980, 52, 71-75
71
Consecutive Amperometric Titrations for Calcium and Magnesium L. L. Jackson,’ Janet Osteryoung,”’ John O’Dea,2 and R. A. Osteryoung2 Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523
Calcium and magnesium are determined in the same sample aliquot by successive titratlon with EGTA and EDTA (or DCTA), respectively, using pulse polarographic amperometric detection of the end point based on mercury oxidation In the presence of excess chelon. Over the concentration range Ca:Mg of 1:O.l to 0.1:0.5 mF, errors are within f l % and standard deviations within 1% for calcium and errors +1-3% with standard deviations within l % for magnesium. Particularly In the automated mode, this method appears attractive for analysis of natural waters and other sample types.
There are many analytical methods for calcium and magnesium, but none has been capable of the measurement of both metal concentrations in a single aliquot. We have developed such a procedure in which calcium is titrated first with ethylene glycol bis(P-aminoethyl ether)-N,NJ”J”-tetraacetic acid (EGTA) and then magnesium is titrated with ethylenediaminetetraacetic acid (EDTA) ( I ) . DCTA (1,2-diaminocyclohexane-N,N,N’,N’-tetraacetic acid) was also examined as a possible titrant for magnesium. T h e end point in each titration is determined by amperometric detection of the excess chelate a t a dropping mercury electrode. The current produced by the reaction
Hgo + HY3-
-
HgY2- + H+ + 2e-
(1)
is plotted vs. the volume of titrant added to give the amperometric titration curve. Several titrimetric methods have been developed for the consecutive determination of calcium and magnesium (2-8). Most have used EGTA as the titrant for calcium and a second chelon such as EDTA or DCTA to titrate the magnesium. Even though some of these methods permit titration of calcium and magnesium in a single sample aliquot, they have not been used routinely. In natural water analysis the standard method is to mask the magnesium in one sample and titrate the calcium colorimetrically. Then in another sample the total of calcium and magnesium is determined, and the magnesium is found by difference (9). The other major technique used is atomic absorption spectrometry in which the two metals are determined independently by utilizing two source lamps. Both techniques suffer from experimental problems. For instance, in the atomic absorption methods, phosphate and sulfate interfere and must be masked. The colorimetric difference methods are inherently bad since any error in the calcium titration is propagated in the magnesium determination. This is an especially serious problem when magnesium is the minor constituent. Several groups have developed amperometric titrations for calcium and magnesium. The work of Fleet et al. (10) and ‘Present address: Allied Chemical Corp., 550 Second Street, Idaho Falls, Idaho 83401. Present address: Department of Chemistry, State University of New York a t Buffalo, Buffalo, N.Y. 14214. 0003-2700/80/0352-0071$01 OO/O
that of Monnier and Roueche (6) are characteristic of the titration schemes used. In Fleet’s method, the calcium is titrated with EGTA and in another sample the total calcium and magnesium are titrated with EDTA. The magnesium is then determined by difference as in the standard colorimetric procedure. Monnier and Roueche titrate the calcium with EGTA as well. Then the magnesium is titrated with EDTA in the same sample. In both methods the end point is indicated by the anodic current produced by excess chelon a t a mercury electrode. However, in the latter method excess EDTA is detected in the presence of excess EGTA. T h a t is, the current measured in the magnesium titration is the sum of the currents due to excess EGTA and excess EDTA. In Fleet’s work, 0.24 F ammonia buffer a t pH 9.8 was used as the supporting electrolyte. In the calcium titration, pentasodium triphosphate was added to mask the magnesium. Also in the EDTA titration for total calcium and magnesium Triton X-100 (0.002%) was added to eliminate the maximum on the EDTA wave. Each titration was performed by making standard additions of the chelon and obtaining a dc polarogram of the solution. In the titration for total calcium and magnesium a t the 0.1 mF level, a n error of 20% was found, while a t 0.8 m F the error was 1.2%. No explanation for the larger error was offered. The EDTA titration of calcium in the presence of magnesium gave errors of 1-6% for calcium to magnesium ratios of 1:l to 1:lO with calcium levels of 0.14.5 mF. At a calcium concentration of 0.1 m F in the presence of 2 m F magnesium, apparently no calcium was found. The standard deviation for sets of three replicates was on the order of 1%. No study of interferences was made. In the procedure developed by Monnier and Roueche, 0.1 F ethanolamine buffer a t pH 10.5 was used. In this buffer the half-wave potentials for EGTA and EDTA differ by only a few millivolts. The chelons were added successively using an automated buret with a magnetic stirrer in the sample to ensure adequate mixing. The current a t a single potential corresponding to the limiting current plateau of the dc polarograms for both chelons was monitored as a function of the volume of titrant added. The indicator electrode was a mercury cup electrode and not a DME as used by Fleet. In general, the error in the calcium titrations was 1-3%. Except a t high calcium to magnesium ratios, the error in the magnesium titration was 2-3%. A t large ratios of calcium to magnesium (i.e., m F concentrations of 3.3/0.033 and 1.66/ 0.166) the error was 10-12%. The standard deviation was about 1-3% for most of the titrations. They applied their procedure to the analysis of blood and urine ( 1 1 ) as well as to water. Several masking agents were also investigated. In particular, a mixture of citrate and tartrate was used to mask iron and triethanolamine was used to mask aluminum. This paper presents a procedure for consecutive amperometric titrations for calcium and magnesium in a single aliquot. Two different chelons were used and the excess chelon in each titration was detected amperometrically. EGTA was used to titrate calcium, and either DCTA or EDTA was used for magnesium. Both the normal pulse and differential pulse amperometric modes were used in contrast to the dc amC 1979 American Chemical Society
72
ANALYTICAL CHEMISTRY, VOL. 52, NO. 1, JANUARY 1980
C
0
1.2
I
100 n A
I
I
I
0
60
120
I 180
TIME, sec
Figure 1. Data analysis by computer. Titration of 0.1 mF magnesium with 5 mF DCTA. Shown are the experimental parameters, titration curve, and titration curve with least-squares lines. Position of cursers is chosen by operator
perometric mode which has been employed in other work. The methods developed were tested at calcium and magnesium levels of 1-0.001 mF. Also, analyses were done a t ratios of calcium t o magnesium from 1OO:l to 1:lOO. Finally, these amperometric techniques were applied to a variety of natural samples.
EXPERIMENTAL Standard chemical procedures and electrochemical techniques and equipment were used. They are described in detail elsewhere ( I , 12,13). In general in the automated titrations drop times of 1 s and normal pulse amplitudes of 250 mV with initial potential -0.350 V vs. SCE were used. A Laitinen-Burdett cell was used to ensure adequate mixing and shielding of the electrode from convection (14). Titrations were carried out either by making standard additions of titrant with microliter pipets and then obtaining a pulse polarogram for each addition or by adding the titrant at a constant rate using a Sargent-Welch Model DG dual buret titrator and monitoring the current continuously at the appropriate potential using either differential or normal pulse polarography. In the automated system starting the titrator, applying the potentials, and making the current measurements were under software control. Typical graphical output illustrating the method of data analysis is shown in Figure 1. The titrant delivery rate was calibrated gravimetrically. In Lising the L-B cell and the titrant delivery system, a large titration blank was obtained due to the finite mixing time. This blank depended on cell size and nitrogen flow rate. At a flow rate of 500 mL/s and with a large L-B cell approximately 3-5 s was required before a rise in current was observed. When 50 pL of titrant was added instantaneously and the data acquisition program was started at the same time, the current rose after 3-5 s, but the maximum current was not obtained until a few seconds later. Thus, the blank is truly a mixing
E , V vs. SCE
Figure 2. Titrations of calcium and magnesium by standard addition using differential pulse polarography. Conditions: pH 9.4, 0.2 F NH3/NH,N0,; drop time = 1 s; scan rate = 1 mV s-'; m = 1.3 mg s-': A € = 10 mV. (A) Titration of 0.1 mF calcium with 5 mF EGTA, (B) titration of 0.1 mF magnesium with 5 mF EDTA, (C) titration curves: ( 0 )calcium, (A)magnesium
phenomenon. Although the blank is larger than would be expected, it is fairly reproducible and can be subtracted out. Two titrant delivery rates were necessary to keep the titration time large with respect to the mixing time: they were 1.33 X lo-* and 2.27 x 10-3 p ~ / s .
RESULTS AND DISCUSSION T h e selection of appropriate chemical and instrumental conditions for the consecutive amperometric titration of calcium and magnesium is described elsewhere (12). In most fresh water samples, calcium and magnesium are present a t concentrations of 0.1 t o 1 mF. Therefore, much of this work has been aimed at developing suitable titrations for 0.1 m F levels of both metals. Typical consecutive differential pulse amperometric titrations for calcium and magnesium by standard additions are shown in Figure 2 . P a r t A displays polarograms with successive addition of EGTA (the calcium titration), and part B displays polarograms with successive addition of EDTA (the magnesium titration). The resulting current-volume curves are shown in part C. The concentration of excess titrant used in these titrations carried out by standard addition corresponds t o the excess used in the automated titrations. For illustrative purposes, a pulse modulation amplitude of 10 mV was used for both titrations. In practice this is not necessary. In the first titration, a larger amplitude could be used since it is necessary only to resolve the peak from the background. In the automated titrations, a pulse amplitude of 25 mV was used in the calcium-EGTA titration and an amplitude of 10 mV was used in the magnesium-EDTA (or DCTA) titration. The standard addition
ANALYTICAL CHEMISTRY, VOL. 52, NO. 1, JANlJARY 1980
73
Table I. Consecutive Titrations for Calcium and Magnesium in the Differential Pulse Amperometric ModeU Mg w/DCTA Ca w/EGTA Mg w/EDTA Ca w/EGTA CaiMg, C X lo4 F % errorb % std. dev. % error % std. dev. % error % std. dev. % error 4; std. dev. lO/l +0.2 0.3 + 7.0 1.9 + 1.0 0.3 -1 2.1 1.2 511 + 0.9 0.4 t4.6 2.7 +0.2 1.0 -t 1.4 1.8 0.7 t0.7 0.8 +2.2 2.1 211 +0.4 0.7 i 2.0 1.4 -0.2 1.0 +1.9 1.1 l/l + 0.4 0.9 + 1.7 0.9 + 0.04 0.5 + 3.5 0.6 1/2 +1.2 0.5 + 1.8 0.4 + 1.0 0.8 -t 4.0 1.0 1.2 i 2.7 115 -0.6 Calchm was titrated with EGTA and magnesium was titrated with EDTA or DCTA. Five replicates of each titration. - X t ) / X t where X is the average value and Xt the true value.
100 ( X
Table 11. Titrations for Calcium and Magnesium in the Absence of Each OtheP Ca2+ EGTA titrantb % error % std. dev.
metal concn., m F
-0.5
1 C
EDTA titrantb % std. dev.
Five replicates of each titration. Normal Pulse Amperometric Mode. 0.1.
DCTA titrantb error % std. dev.
~~-
% error
+ 0.9 + 2.1 + 1.9 + 14
0.3 0.5 0.7 2.8
+ 0.4 +3.2 + 33
0. I d O.Ole O.OOle
Mgz+ %
+ 2.9 + 2.8 19.6 + 23
0.3 0.3 1.4 6.6
0.7
0.5 0.7 7.0
Titrant concentration, mF: ( c ) 10, ( d ) 5, ( e )
Table 111. Consecutive Titrations for Calcium and Magnesium in the Normal Pulse Amperometric ModeU Ca w/EGTA Mg w/EDTA Ca w/EGTA Mg w/DCTA CaiMg, C x 10' F % error % std. dev. % error % std. dev. % error 76 std. dev. 'To error % std. dev. lO/O.l lO/l
511 211 l/l
1/2
l/5 1/10
0.3 0.3 0.5 0.5 0.4 0.3 1.2
-0.2
0.5
+ 5.5
O.l/lO CI
-0.5 -0.03 +0.4 +0.3 +0.8 -0.3 -1.3
-27 +0.6
+ 1.1 + 1.2 + 2.4 + 2.6 + 3.0 + 2.5 +0.9
1.3
9.2 1.2 0.5 0.5
-0.3
0.2
-0.2 -0.1 -1.4
0.5 0.3 0.7
0.5 0.5 0.7
-1.1
0.4
+ 2.3
+0.4
0.4
+0.5
0.8 0.8
+3.5 + 2.9
0.3
___
2.5 0.3 0.8 0.3 0.4 1.2 0.4 0.1
-0.7 +1.9 + 2.6 ?- 2.4
0.2
+ 0.02
2.1
___
.__
_--
Calcium was titrated with EGTA and magnesium was titrated with EDTA and DCTA. Five replicates of each titration.
EDTA Ca/Mg, C
x l o 4 F %error 1/10
o/ 1 l/l
+ 3.3 i 2.4
+3.5
DCTA std. dev.
%error
std. dev.
1-2.2 t3.2 +2.7
0.6 0.6
%
0.8
0.5 0.2
%
.'
C
Table IV. Hardness Titrations with EDTA and DCTA in the Normal Pulse Amperometric Mode"
A
.- .-.-.--.+ 0
I
4
.
8
I2
0.5
Five replicates of each titration. titrations for calcium and magnesium at the 0.1 m F level were generally accurate within 3% and the standard deviation for three titrations was less than 1% . T h e results of automated titrations a t various calcium to magnesium ratios with EGTA as the calcium titrant and EDTA or DCTA as the magnesium titrant are given in Table I. T h e calcium titrations in the concentration range 0.1-1 m F were within 1%of the known value with a standard deviation of about 1% or less. Thus, there was essentially no methodological error in the calcium titrations since the results fell within the confidence limits of the measurement. T h e error in the magnesium titrations varied from 1-770with the standard deviation as large as 3%. In the normal pulse mode, standard addition titrations were obtained as shown in Figure 3. The current was measured at a single potential in the plateau region of the EGTA, EDTA,
-03
- 0 2 5 - 0 2 -015 -01 E , V vs SCE
-005
Flgure 3. Titrations of calcium and magnesium by standard addition using normal pulse polarography. Conditions as Figure 2. (A) Titration of 0.1 mF calcium with 5 mF EGTA, (B) titration of 0.1 mF magnesium with 5 mF EDTA, (C) titration curves: ( 0 )calcium, (A)magnesium
and DCTA waves. Thus, for the calcium determination the current depended on the concentration of excess EGTA, while
74
ANALYTICAL CHEMISTRY, VOL. 52, NO. 1, JANUARY 1980
in the magnesium titration the current was due to the sum of the excess EGTA and DCTA (or EDTA). The results of the automated normal pulse mode titrations are given in Tables 11-IV. In Table I1 are listed the results obtained for calcium and magnesium titrations each in the absence of the other metal. As seen in this table, acceptable results were obtained at metal concentrations of 0.01 m F and larger. At a concentration of 0.001 mF, large positive errors occurred. This was also the case for the titration of magnesium with DCTA a t a concentration of 0.01 mF. The reasons for these large positive errors were not readily apparent and their elucidation was not pursued. Table I11 gives the results for consecutive titrations of calcium and magnesium a t ratios from 1OO:l to 1:lOO. As in Table I, the calcium titrations were accurate within 1% with the standard deviation generally less than 1%.In the magnesium titrations with both EDTA and DCTA the error was usually 2-3 % while the standard deviation was about 1% , In comparing the results in Tables I1 and 111, the calcium titrations were about the same with or without magnesium present. The magnesium results were also about the same except when calcium was present in large excess. When titrating magnesium a t 0.01 m F with no calcium present the error was about 2% and 10% when titrating with EDTA and DCTA, respectively. When calcium was present at 1 mF, the error in the magnesium titration was -27% and -1% with EDTA and DCTA, respectively. This large discrepancy was not explainable on the basis of the data available. As should be obvious, both EDTA and DCTA are good titrants for total hardness. Table IV presents the results for hardness titrations using the normal pulse mode. Similar results were obtained using the differential pulse mode. Since only one chelon wave need be monitored in hardness determinations, larger pulse modulation amplitudes can be used than in the consecutive titrations. The error in the normal pulse titrations was +3%. This error is the same as found in the magnesium titrations with EDTA and DCTA. The standard deviation for five determinations was less than 1% . Interlaboratory studies employing EDTA titration with visual indicator end point for hardness determination in samples 0.2-4 m F in Ca(I1) gave negative errors in the range of 0.2-3.2% and standard deviations in the range 2-8% (15). T h e errors in the titrations can arise from several sources: the standardization of the titrants and metal solutions; the use of microliter pipets and the auto-titrator; determination of the blank; uncertainty in the end-point calculation; and various solution phenomena. Methodological errors are emphasized here because standardizations are done by colorimetric titration. In practice, the amperometric procedure used in the determination would also be used in the standardization and this would tend to eliminate systematic error. The standard deviation in the determination of the blank varied from 10 to 30%; however, by keeping the titration time large with respect to the mixing time, one can make this error small in comparison with the total error. Chemical phenomena could be large sources of error. For instance, complexation of magnesium by EGTA could cause error in the calcium titration. This was not found to be the case. The exchange of calcium between EGTA and the magnesium titrant is another possible source of error. Monnier and Roueche claim this exchange does not occur (6). However, as shown by differential pulse polarograms of a solution of free EDTA to which Ca-EGTA was added, the exchange does occur to a considerable extent. Under the conditions of the titration, similar polarograms were obtained with DCTA and Ca-EGTA. This exchange could account for a positive error in the titrations employing differential pulse end-point detection. On
the other hand, in the titrations employing normal pulse, the exchange should not affect the results. If all of the magnesium were chelated by EDTA (or DCTA) prior to any exchange, then current would be produced a t the magnesium titration end point due to either the excess EDTA or the released EGTA. In either case, the end point should be indicated accurately by the rise in current. If all the sources of error are considered, results within a few percent would appear quite acceptable. As mentioned previously, in the calcium titrations with EGTA the errors were fl%, but in the magnesium titrations with either EDTA or DCTA the error was usually +2-3%. The same results were obtained if EDTA or DCTA was used to titrate calcium. Since the errors in the consecutive titrations were comparable with those for the visual colorimetric methods and the other amperometric techniques, no further attempts a t eliminating or defining the sources of error were made. Differential and normal pulse end-point detection give about the same error; however, for routine analysis the normal pulse mode has several advantages over the differential pulse mode. First of all, the exchange of calcium between EGTA and the magnesium titrant should not be a source of error in this mode. Second, the presence of surfactants affects the differential pulse waves more severely than it does the normal pulse waves (12). Analysis of samples with unknown amounts of surfactants in the differential pulse mode would require that the peak potential of the titrants be measured in a separate aliquot of sample prior to the actual titration. In the normal pulse mode, this would not be a serious problem, since the limiting current region of the chelon waves was affected very little by the presence of surfactants. Thus, the normal pulse mode is a more reliable and convenient technique for end-point detection. Applications. The consecutive determination of calcium and magnesium, the determination of either metal in the presence of the other, and the determination of the total of both metals have a large number of possible applications. The primary application considered in our work has been to water analysis. In fresh waters the calcium and magnesium concentrations usually range from 0.1-1 m F with the calcium concentration greater than the magnesium concentration. In seawater the opposite is true. The magnesium concentration is 0.05 F and the calcium concentration is 0.01 F. Most other metals, except Na and K, are found at trace levels, 0.001-0.01 mF, in both fresh and salt water. Thus, interferences in the determination of calcium and magnesium due to other metals normally do not present a problem, except when visual indicators are used. In that case even trace levels of some metals interfere with the end point by chelation with the indicator. When these extraneous metals are present a t high concentrations they are titrated along with the calcium and magnesium. In hardness titrations, these metals should be included, but in practice they are masked to prevent interference with the indicator reaction. In hardness titrations with amperometric end-point detection, this problem does not occur. Nevertheless, for the consecutive determination of calcium and magnesium, several masking agents were examined. In the past it has been said that cyanide or similar masking agents which gave an anodic mercury wave could not be used in the amperometric determination of calcium and magnesium. In principle if cyanide were added to a sample with only a small excess, and the metal-CN complex did not react with EGTA or EDTA, both calcium and magnesium could be titrated in the normal pulse mode. In this case the background current would be higher owing to the constant level of free cyanide. Instead of trying cyanide as a masking agent, because of the toxicity of HCN we tested tetraethylenetriamine (TRIEN). This chelon has a large formation constant for
ANALYTICAL CHEMISTRY, VOL. 52, NO. 1, JANU.4RY 1980
Table V. Analysis of Water SarnplesU [Ca], mF EPA 1 EPA 2
simulated seawater
0.362 1.11 10
7c % std. [Mg], error dev. mF
-1.9 -2.3 +2.0
0.3 0.4 0.2
0.123 0.592 53
7% 7% std. error dev. -3.6 -2.6 -0.4
4.6 0.7 0.2
EGTA and EDTA used as titrants in the normal pulse amperometric mode, each 5 m F ; 0.2 F NH,/NH,NO,, pH 9.4: five reolicates of each titration.
mercury and several other metals, and it does not chelate with calcium or magnesium. In titrations of separate solutions of calcium and magnesium (each a t 0.1 mF), copper a t 10 ppm (0.16 mF) was masked quantitatively by TRIEN. Nickel, also a t 10 ppm (0.17 mF), was masked only in the calcium titration and caused a 2% error in the titration result for calcium. Both metals in the same solution a t 10 ppm were satisfactorily masked as well in the calcium titration. Zinc a t 0.1 m F was masked in the calcium titration, but the total zinc and magnesium were titrated with EDTA. Similar results were obtained for cobalt. In titrations with cadmium present a t 10 ppm, large errors were found in the calcium titration, but EGTA and T R I E N masked the cadmium in the magnesium titration. T R I E N was present a t 0.504.1 m F in excess of the interfering metals in these titrations. Larger metal and TRIEN concentrations could presumably be tolerated in the titrations without severely affecting the results. Direct titrations of chromium, iron, and lead, each at 10 ppm, were attempted with EDTA. However, since the solubility of each metal hydroxide was exceeded, none of the metals were detected. On the time scale of the titrations, none of the hydroxide species dissolved in the presence of EDTA. Iron and aluminum have been masked by triethanolamine (16). We found no iron interference in the calcium and magnesium titrations when iron was present a t 10 ppm (0.18 mF) a t a triethanolamine concentration of 10 mF. Several anions could cause interferences. If the phosphate or sulfate concentration were high enough, calcium salts would be precipitated. Thus, the use of these anions in the supporting electrolyte or buffer solutions should be avoided. In the past, chloride has also been avoided in amperometric titrations with a mercury indicator electrode. In our work concentrations of chloride u p to 10 m F did not interfere. In summary, it is possible to mask copper and nickel with TRIEN. Excess T R I E N does not have an adverse effect on the calcium and magnesium titrations in the normal pulse mode. In this mode, exchange of a metal complexed to T R I E N with EGTA or EDTA will cause an increase in current. If the calcium or magnesium is complexed prior to the exchange, the increase in current due to the TRIEN released will signal the titration end point as in the case of exchange of calcium between the EGT.4 and EDTA in the magnesium titration. Iron and aluminum can be masked with triethanolamine. Suitable masking agents were not found for cadmium and zinc, but they cannot be masked in the visual titrations either. In the amperometric titrations, cadmium mas titrated with calcium: although not quantitatively, while zinc was titrated quantitatively with magnesium.
75
T o examine the general methodology, several water samples were titrated with EGTA and EDTA using the normal pulse mode. ijCTA was not considered to offer any significant advantages over EDTA as a magnesium titrant, and so it was not used. Two of the water samples analyzed were obtained from the Environmental Protection Agency's quality control program. These samples were concentrates that when made up to volume were characteristic of hard and soft water with all of the major constituents normally found in fresh water (trace metals were omitted). The third sample was a simulated seawater sample prepared from reagent grade chemicals and diluted to volume with distilled-deionized water with a resulting salinity of 34% (17). The results of the analyses are given in Table V. Five milliliters of the EPA water samples and 250 FL of the seawater sample were titrated in 50 mL of ammonia buffer. Each titration was performed five times. Considering the nature of the samples, the results are quite acceptable. Thus, consecutive titrations for calcium and magnesium on a routine basis for both fresh and salt waters would appear feasible using these methods. In comparing the pulsed amperometric procedures with previous amperometric methods for calcium and magnesium determinations there are several distinct differences. First of all, the pulsed amperometric modes are more sensitive than the dc mode used in other methods. Second, both the calcium and magnesium are determined directly as opposed to using a difference technique in the fashion of Fleet (10). Although the methodology is similar to that developed b:y Monnier and Roueche ( 6 ) ,the accuracy and precision of the titrations was improved owing to better understanding of the chemical phenomena occurring during the titration and their effect on the results. At this point it appears, that the I.imiting factor in accuracy, precision, ease of use, and cost of this approach lies in mechanical problems of cell design and titrant delivery.
ACKNOWLEDGMENT The authors acknowledge the assistance of James Dillard in developing the computer programs used in this work. LITERATURE CITED L. L. Jackson, Ph.D. Thesis, Colorado State University Fort Collins, Colo.,
1978. H. Sato and K. Momoki, Anal. Chem., 44, 1778 (1972). K. Toei and T. Kobatake, Talanta, 14, 1354 (1967:'. 6 . Van't Reit and J. Wynn, Anal. Chem., 41, 158 11969). C. Huber, K. Dahnke, and F. Hinz, A n d . Chem., 43, 152 (1971). D. Monnier and A. Roueche, Helv. Chim. Acta, 47, 103 (1964). T. Christiansen, J. Busch, and S. Krogh, Anal. Chem., 48, 1051 (1976). R. Callicott and P. Carr, Clin. Chem., 22, 1084 (lCl76). M. Taras, Ed., "Standard Methods for the Examination of Water and Wastewater", 13th ed., American Public Health Association, New York,
1970. 6 . Fleet, S. Win, and T. West, Analyst (London),94. 269 (1969). D. Monnier and A. Roueche, Helv. Chim. Acta, 47, 369 (1964). L. L. Jackson, Janet Osteryoung, and FI. A. Osteryoimg, Anal. Chem., following paper in this issue. J. A. Turner, Ph.D. Thesis, Colorado State University, Fort Collins, Colo.,
1977. H. Laitinen and L. Burdett, Anal. Chen?., 22, 833 (1950). J. A . Winter and M. R. Midgett, FWPC4 Method StlJdy 1, Mineral and Physical Analyses AQCL, Cincinnati, Ohio, 1969. D. Perrin, "Masking and Demasking of Chemical Reactions", Interscience, New York, 1970. C. Stephan, fnvir. Prof. Agency(U.S.) Rep., EPA-660/3-75-009, 1975.
RECEIVED March 8, 1979. .4ccepted October 15, 1979. This work was supported by the National Science Foundation under grant C H E 7500332.
